if ef=2x-19, fg=3x-16, and eg=25, find the values of x, EF, and FG
ef+fg=eg, so
2x-19+3x-16=25, go from there
To find the values of x, EF, and FG, we will use the given equations and solve step by step.
Given equations:
1) EF = 2x - 19
2) FG = 3x - 16
3) EG = 25
Step 1: Find the value of x
The value of x can be found by equating EF and EG:
EF = EG
2x - 19 = 25
To isolate x, we will add 19 to both sides of the equation:
2x = 25 + 19
2x = 44
Divide both sides of the equation by 2 to solve for x:
x = 44 / 2
x = 22
So, the value of x is 22.
Step 2: Find the value of EF
Now that we know the value of x, we can substitute it into one of the equations (let's use equation 1: EF = 2x - 19) to find the value of EF:
EF = 2(22) - 19
EF = 44 - 19
EF = 25
So, the value of EF is 25.
Step 3: Find the value of FG
To find the value of FG, we can substitute the value of x (which is 22) into equation 2: FG = 3x - 16:
FG = 3(22) - 16
FG = 66 - 16
FG = 50
So, the value of FG is 50.
Therefore, the values of x, EF, and FG are:
x = 22
EF = 25
FG = 50